Answer: The domain of f-1(x) is all real numbers and the range is all real numbers greater than 0.
Step-by-step explanation:
The inverse function of f(x) = ln(x) is:
f-1(x) = exp(x).
And as:
The domain of f(x) is: x ∈ R, x > 0.
The range of f(x) is: x ∈ R
Then for the inverse, we should have the opposite:
The domain of f-1(x) is: x ∈ R (the exponential function does not have any problems like the logarithm, so you can actually input any real value).
The domain is: x ∈ R, x > 0.l
Because, for example:
e^0 = 1
e^-1 = 1/e > 0.
e^-n = 1/e^n > 0.
e^x is always positive, then the range is the set of all real numbers large than zero.
